Reconstruction and restoration of two polarization components of an optical signal field

ABSTRACT

A digital version of both amplitude and phase of at least one generic polarization component of a received optical signal is developed using dual-polarization direct differential detection with digital signal processing. The received signal is split into orthogonal polarization components, each of which is split into three copies. For each orthogonal polarization component a) an intensity profile is conventionally obtained using a copy and b) phase information is obtained by supplying each remaining copy to a respective one of a pair of optical delay interferometers having orthogonal phase offsets, followed by respective balanced intensity detectors. The outputs the balanced intensity detectors and the intensity profiles are converted into digital representations and used to develop, via signal processing, the optical field information of at least one generic polarization component of the received optical signal. Compensation of impairments, such as PMD, is realized through further processing.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of U.S. provisional patent applicationSer. No. 60/993,823, filed Sep. 14, 2007, which is herein incorporatedby reference.

TECHNICAL FIELD

This invention relates to the reconstruction of the two polarizationcomponents of an optical signal field and compensation forpolarization-mode dispersion.

BACKGROUND OF THE INVENTION

As is well known, an optical signal may have two orthogonal polarizationstates, each of which may have different properties. Sometimes suchpolarization states are intentionally introduced, such as in creating apolarization-multiplexed signal in which the two orthogonal polarizationstates of the optical carrier are arranged so that each carriesdifferent data in order to double the spectral efficiency. Such apolarization-multiplexed signal has two so-called “generic” polarizationcomponents, each of which carries a single data modulation. Note that bya generic polarization component it is generally intended the signal atthe point at which the modulation of that polarization component iscompleted. It should be appreciated that each generic polarizationcomponent may initially, or otherwise, exist separate from the othergeneric polarization component with which it is later combined.

The polarization orientations of the generic signal components aregenerally changed by the birefringence of the fiber, and possibly otherfiber properties, during the passage of the signal over the opticalpath. Such changes may be time varying because at least the fiberbirefringence is typically a function of various factors such as ambienttemperature, mechanical stress, and so forth, which may vary over timeand be different at various points of the transmission path. As aresult, the polarization orientation of each of the generic signalcomponents is generally unknown at the receiver.

Sometimes, undesirably, the fiber birefringence is so large thatpolarization-mode dispersion (PMD) is caused, i.e., a generic opticalsignal component is decomposed into two orthogonal polarizationcomponents along the two principle state of polarization (PSP) axes ofthe fiber, along one of which the light travels at its fastest speedthrough the fiber and along the other of which the light travels at itsslowest speed through the fiber. In such a case, not only may the phaserelationship between the two polarization components be time varying,but also each of the two orthogonal polarization components may arriveat the receiver at different times due to the PMD-induced differentialgroup delay (DGD) between the two PSP axes. Note that, actually, assuggested above, each small section of the fiber behaves as if it is itsown mini fiber that introduces its own DGD between the two PSP axes.However, for simplification purposes, one may treat the fiber as asingle DGD element that introduces a certain DGD between the two axes,based on a first order approximation of the PMD. Thus, for a particularfiber or optical link, PMD is a stochastic effect, and the PMD-inducedDGD may also be time varying.

Other linear effects distort optical signals transmitted over opticalfibers. Such effects include chromatic dispersion (CD). Opticalcompensation methods are typically employed to reduce signal distortionthat arises due to CD or PMD.

Electronic chromatic dispersion compensation (EDC) has recently emergedas a technique that can flexibly reduce the distortion induced by CD ina cost effective manner. As explained by M. S. O'Sullivan, K. Roberts,and C. Bontu, in “Electronic dispersion compensation techniques foroptical communication systems,” ECOC'05, paper Tu3.2.1, 2005, EDC can beperformed at the transmitter. Alternatively, EDC can be performed at thereceiver. As described by S. Tsukamoto, K. Katoh, and K. Kikuchi, in“Unrepeated Transmission of 20-Gb/s Optical QuadraturePhase-Shift-Keying Signal Over 200-km Standard Single-Mode Fiber Basedon Digital Processing of Homodyne-Detected Signal for Group-VelocityDispersion Compensation,” IEEE Photonics Technology Letters, Volume 18,Issue 9, 1 May 2006, pp. 1016-1018, EDC is implemented with acoherent-detection receiver. In addition, EDC can be implemented with aspecial direct differential detection receiver as explained by X. Liuand X. Wei, in U.S. patent application Ser. No. 11/525,786 entitled“Reconstruction and Restoration Of Optical Signal Field”, filed on Sep.22, 2006 and assigned to Lucent Technologies, which is incorporated byreference as if set forth fully herein and shall be referred tohereinafter as Liu-Wei.

Unlike CD, PMD in a fiber link may change very rapidly and PMDcompensation usually has to be done in the receiver. Electronic PMDcompensation (EPMDC) has also attracted attention recently for itspotential cost effectiveness. As explained by J. Hong, R. Saunders, andS. Colaco, in “SiGe equalizer IC for PMD Mitigation and SignalOptimization of 40 Gbits/s Transmission”, published in Optical FiberCommunication Conference 2005, paper OWO2. However, the capability ofthe EPMDC with a conventional direct-detection receiver is quite limitedin that the improvement in PMD tolerance is usually only about 50%.

SUMMARY OF THE INVENTION

In accordance with the principles of the invention, a digital version ofthe complex field, i.e., both amplitude and phase, e.g., with respect toa reference point, of each of two orthogonal polarization components ofa received optical signal are developed at a receiver by employing adual-polarization direct differential receiver portion that uses directdifferential detection to develop a digital representation of opticalsignals derived from each of two orthogonal polarization components of areceived optical signal which are then processed using digital signalprocessing (DSP) to develop a digital representation of an intensity anda phase profile representing the polarizations as received at thereceiver. The reconstructed digital versions of the complex field ofeach of the two orthogonal polarization components of the optical signalas received at the receiver are then be further processed jointly todevelop at least one so-called “generic” polarization component of thereceived optical. Note that due to fiber birefringence or PMD, the twoorthogonal polarization components of the optical signal as received atthe receiver after fiber transmission are generally not the genericpolarization components of the signal. In accordance with an aspect ofthe invention, during the joint processing the relative phase differencebetween the two reference points used in the two reconstructed opticalfields is determined. This may be achieved by employing a searchingtechnique.

In one embodiment of the invention, a polarization beam splitter (PBS)is first used to separate the received optical signal into twoarbitrarily orthogonal polarization components, E_(x′) and E_(y′). Eachof the orthogonal polarization components is supplied to a specialdirect differential detection receiver, which employs a special pair ofoptical delay interferometers (ODIs) with a phase delay difference ofabout π/2, such as are described in Liu-Wei and which are hereinreferred to as an I/Q ODI pair. At least the four outputs of each I/QODI pair are then detected by two balanced detectors, whose two outputsare sampled by respective analog to digital converters (ADCs), are thenprocessed to obtain a digital representation of the received signaloptical field along the corresponding polarization axis, i.e., x′ or y′,according to Liu-Wei.

In a second embodiment of the invention, the received optical signal issupplied directly into a single polarization-independent I/Q ODI pairand the resulting four outputs are each connected to a respectiveassociated one of four PBSs, all of which have the same polarizationorientation. Each of the PBS produces two outputs, so that in totalthere are eight outputs from the four PBSs, consisting of four outputsderived from the first polarization, e.g., x′-polarized outputs, andfour outputs derived from the second polarization, e.g., y′-polarizedoutputs. Each pair of outputs of the PBSs that corresponds to a singleoptical delay interferometer and a single polarization are supplied to arespective one of four balanced detectors, whose outputs are sampled bya respective one of four corresponding ADCs. Each of the resultingsampled waveforms are then processed to obtain a digital representationof the received signal's optical field along each of the polarizationaxes x′ and y′ in the manner described in Liu-Wei.

Even though this second embodiment requires the use of three additionalPBSs as compared to the first embodiment, due to the relative cost ofI/Q ODIs themselves and the control electronics associated therewith, ascompared to the cost of PBSs, advantageously, because only one I/Q ODIpair is employed, significant cost savings can be achieved. Furthermore,the second embodiment may be more compactly implemented.

Either embodiment of the invention may be implemented with free space orfiber based optics, or any combination thereof.

Although to save cost it is expected that implementers generally willapproximate the intensity profile of one or more of the polarizationcomponents of the received signal from the absolute value of theirrespective complex waveforms, they may instead employ direct intensitydetection to obtain a more accurate measurement of the intensityprofile.

The techniques of the instant invention are suitable to be employed withvarious types of optical differential phase-shift keying (DPSK) signals,such as differential binary phase-shift keying (DBPSK) and differentialquadrature phase-shift keying (DQPSK) signals. They may also be employedwith amplitude-shift keying (ASK), combined DPSK/ASK, and quadratureamplitude modulation (QAM).

BRIEF DESCRIPTION OF THE DRAWING

In the drawing:

FIG. 1 shows an exemplary apparatus, typically in a receiver, arrangedin accordance with the principles of the invention, for developing atleast one so-called “generic” polarization component of a receivedoptical signal;

FIG. 2 shows an embodiment of the invention similar to that shown inFIG. 1 but in which the intensity detection branches are omitted;

FIG. 3 shows another embodiment of the invention similar to that shownin FIG. 1 but which employs only a single I/Q ODI pair;

FIG. 4 shows an exemplary polarization “evolution” as an optical signalpasses over a typical fiber transmission link that causes PMD;

FIG. 5 shows an exemplary arrangement to perform the digital signalprocessing needed to recover the generic polarization components fromthe reconstructed optical fields of the two orthogonal polarizationcomponents of the received optical signal, in accordance with an aspectof the invention;

FIG. 6 shows an exemplary high level block diagram of an arrangementwhich is suitable to be used to make up each of the processing units ofFIG. 5;

FIG. 7 shows an exemplary process expressed in flow-chart form forfinding the best guesses of the parameters needed to recover E_(x)(t)and E_(y)(t), in accordance with an aspect of the invention;

FIG. 8 shows an exemplary process, expressed in flow-chart form, whichis performed by the real-time subprocessor 602 of FIG. 6 in oneembodiment of the invention;

FIG. 9 shows an exemplary high level block diagram arrangement that issuitable to be used to make up each of the processing units of FIG. 5but which is arranged to speed up the processing as compared to thearrangement shown in FIG. 6;

FIG. 10 shows exemplary high level block diagram of an arrangementsuitable to be used to make up each of the processing units of FIG. 5but which is arranged to treat the fiber as if it was made up ofmultiple segments, so as to achieve better compensation for PMD,including higher order PMD, than can be achieved than using thearrangements of FIG. 6 or 9;

FIG. 11 shows high level block diagram of an arrangement suitable to beused to make up each of the processing units of FIG. 5 but which isarranged to treat the fiber as if it was made up of 2 segments eachhaving DGD values each fixed to 0.4 T_(S).

FIG. 12 shows an exemplary high level block diagram of an arrangementwhich is suitable to be used to make up each of the processing units ofFIG. 5 but which is arranged for use with a coherent-detection receiver,in accordance with an aspect of the invention; and

FIG. 13, shows an exemplary process, expressed in flow-chart form, thatis performed in the real-time subprocessor of FIG. 12, in one embodimentof the invention.

DETAILED DESCRIPTION

The following merely illustrates the principles of the invention. Itwill thus be appreciated that those skilled in the art will be able todevise various arrangements that, although not explicitly described orshown herein, embody the principles of the invention and are includedwithin its spirit and scope. Furthermore, all examples and conditionallanguage recited herein are principally intended expressly to be onlyfor pedagogical purposes to aid the reader in understanding theprinciples of the invention and the concepts contributed by theinventor(s) to furthering the art, and are to be construed as beingwithout limitation to such specifically recited examples and conditions.Moreover, all statements herein reciting principles, aspects, andembodiments of the invention, as well as specific examples thereof, areintended to encompass both structural and functional equivalentsthereof. Additionally, it is intended that such equivalents include bothcurrently known equivalents as well as equivalents developed in thefuture, i.e., any elements developed that perform the same function,regardless of structure.

Thus, for example, it will be appreciated by those skilled in the artthat any block diagrams herein represent conceptual views ofillustrative circuitry embodying the principles of the invention.Similarly, it will be appreciated that any flow charts, flow diagrams,state transition diagrams, pseudocode, and the like represent variousprocesses which may be substantially represented in computer readablemedium and so executed by a computer or processor, whether or not suchcomputer or processor is explicitly shown.

The functions of the various elements shown in the FIGs., including anyfunctional blocks labeled as “processors”, may be provided through theuse of dedicated hardware as well as hardware capable of executingsoftware in association with appropriate software. When provided by aprocessor, the functions may be provided by a single dedicatedprocessor, by a single shared processor, or by a plurality of individualprocessors, some of which may be shared. Moreover, explicit use of theterm “processor” or “controller” should not be construed to referexclusively to hardware capable of executing software, and mayimplicitly include, without limitation, digital signal processor (DSP)hardware, network processor, application specific integrated circuit(ASIC), field programmable gate array (FPGA), read-only memory (ROM) forstoring software, random access memory (RAM), and non-volatile storage.Other hardware, conventional and/or custom, may also be included.Similarly, any switches shown in the FIGS. are conceptual only. Theirfunction may be carried out through the operation of program logic,through dedicated logic, through the interaction of program control anddedicated logic, or even manually, the particular technique beingselectable by the implementor as more specifically understood from thecontext.

In the claims hereof any element expressed as a means for performing aspecified function is intended to encompass any way of performing thatfunction. This may include, for example, a) a combination of electricalor mechanical elements which performs that function or b) software inany form, including, therefore, firmware, microcode or the like,combined with appropriate circuitry for executing that software toperform the function, as well as mechanical elements coupled to softwarecontrolled circuitry, if any. The invention as defined by such claimsresides in the fact that the functionalities provided by the variousrecited means are combined and brought together in the manner which theclaims call for. Applicant thus regards any means which can providethose functionalities as equivalent as those shown herein.

Software modules, or simply modules which are implied to be software,may be represented herein as any combination of flowchart elements orother elements indicating performance of process steps and/or textualdescription. Such modules may be executed by hardware that is expresslyor implicitly shown.

Unless otherwise explicitly specified herein, the drawings are not drawnto scale.

In the description, identically numbered components within differentones of the FIGs. refer to the same components.

FIG. 1 shows an exemplary apparatus, typically in a receiver, arrangedin accordance with the principles of the invention, for developing atleast one so-called “generic” polarization component of a receivedoptical signal. This is achieved by developing an electronic version ofthe entire complex optical field of a received optical signal byemploying direct differential detection in conjunction with digitalsignal processing. It is further possible to compensate for variousimpairments that were inflicted upon the optical signal as it traveledfrom its source. FIG. 1 shows a) polarization beam splitter (PBS) 101;b) 1×3 optical splitters 102 and 103; c) optical delay interferometers(ODIs) 105, 106, 107, and 108; d) balanced intensity detectors 111, 112,113, and 114; e) single intensity detectors 115 and 116; f) optionalamplifiers 121, 122, 123, 124, 125, and 126; g) optional automatic-gaincontrollers (AGCs) 131, 132, 133, 134, 135, and 136; h)analog-to-digital converters (ADCs) 141, 142, 143, 144, 145, and 146;and i) digital signal processing (DSP) unit 150.

More specifically, polarization beam splitter 101 separates the receivedoptical signal to produce two orthogonal polarization components, E_(x′)and E_(y′) therefrom. E_(x′) is supplied to 1×3 optical splitter 102while E_(y′) is supplied to 1×3 optical splitter 103. However, theorthogonal polarization components, E_(x′) and E_(y′) are highlyunlikely to correspond to the polarization of the generic componentsthat were originally transmitted as they are currently manifest in thereceived signal.

1×3 optical splitter 102 replicates the received optical signal so as toproduce three copies. One of the three beams produced by 1×3 opticalsplitter 102 is supplied to optical delay interferometer (ODI) 105,another of the three beams produced by 1×3 optical splitter 102 issupplied to ODI 106, and the last beam is supplied to photodiode 115.The optical power allotted to each of the copies from the originallyinput optical signal is at the discretion of the implementer. In oneembodiment of the invention, the power is divided up so that aboutbetween 40 to 45 percent of the input power is supplied as output toeach of ODIs 105 and 106 and the remaining power, e.g., between 10 and20 percent, is supplied to photodiode 115.

As will be readily recognized by those of ordinary skill in the art,optical delay interferometers (ODIs) 105, 106, 107 and 108 may be anytype of interferometer having the required characteristics. For example,the ODIs may be based on the well-known, so-called Mach-Zehnderinterferometer. Alternatively, the ODIs may be based on the well-known,so-called Michaelson interferometer. Preferably, ODIs 105 and 106 aremade in a pair so that their phase orthogonality (or π/2 offset in theirdifferential phases between interfering arms) is automaticallyguaranteed, e.g., using techniques such as disclosed in U.S. patentapplication Ser. No. 10/875,016 applied for on Jun. 23, 2004 byChristopher R. Doerr and Douglas M. Gill, entitled “Apparatus and Methodfor Receiving a Quadrature Differential Phase Shift Key ModulatedOptical Pulsetrain” published as 2005/0286911 on Dec. 29, 2005 and U.S.patent application Ser. No. 11/163,190 applied for on Oct. 8, 2005 byXiang Liu, entitled “Optical Demodulating Apparatus and Method”published as 2007/0081826 on Apr. 12, 2007. Further preferably, the twoODI pairs are either monolithically integrated on a same substrate sothat their characteristic polarization orientations are the same. Notethat the characteristic polarization orientations of an ODI is analogousto the PSP of a fiber.

Each of the ODIs 105 and 107 has a delay of about ΔT in the optical pathbetween its respective two arms and a phase difference, i.e., offset, ofφ₀, where

$\begin{matrix}{{{\Delta\; T} = \frac{T_{S}}{sps}},} & (1)\end{matrix}$where T_(S) is the symbol period of the signal, sps is the number ofsamples per symbol taken by the analog to digital converters and φ₀ isan arbitrarily selected number, which is preferably set at π/4. If so,the free spectral range (FSR), i.e., 1/ΔT, of the ODIs is related to thesignal symbol rate (SR) as FSR=SR·sps. Note that, based on numericalsimulations, it has been found that, preferably, sps be set to a valueof 4. This is because an sps value of less than 4 tends to not besufficient to accurately represent the signal waveform sufficientlygiven the procedures described hereinbelow, while sps greater than 4provides only negligible improvement.

The delay difference may be achieved, in one embodiment of theinvention, by adjusting one arm of the interferometer to have a grosslength difference of ΔT*C/n, where C is the speed of light in vacuum andn is the index of refraction of the medium of the arm, and thenadjusting the length further to cause a phase shift of φ₀. Note that inpractice, because a phase shift of φ₀ corresponds to a very small lengthdifference, the phase shift portion may actually be somewhat longer orshorter, so that the total length is φ₀ plus or minus a multiple of 2π.That way, even thought the length is not precisely φ₀, the phase changeis effectively φ₀.

The total length change used to achieve the effective length change ofφ₀ may be some percentage of the length ΔT·C/n. While even up to 25percent can work, preferably, the percentage is less than 10 percent,and of course, the more accurate the length can be made to match theactual desired length the better the performance will be. In otherembodiments of the invention, the delay required may be divided betweenthe arms, so long as the required delay and phase difference isachieved. Those of ordinary skill in the art will readily recognize howto develop an appropriate arrangement to implement ODIs 105 and 107.

While any value may be employed as the value of phase offset φ₀, forcompatibility with conventional receivers, as will be seen hereinbelow,certain values of φ₀ may be advantageously employed. For example, a goodvalue of φ₀ is π/4 for DQPSK and 0 for DBPSK.

Each of ODIs 106 and 108 are similar to ODIs 105 and 107, in that eachhas delay of about ΔT in the optical path between their respective twoarms, but between their arms they each have a phase offset of φ₀−π/2.Thus, the difference between the phase offsets of ODIs 105 and 106 isπ/2, so ODIs 105 and 106 are said to have orthogonal phase offsets.Similarly, the difference between the phase offsets of ODIs 107 and 108is π/2, so ODIs 107 and 108 are said to have orthogonal phase offsets.

Together, ODI 105 and 106 make up a so-called “I/Q ODI pair”. The fouroutputs of I/Q ODI pair made up of ODIs 105 and 106 are then detected bytwo balanced detectors 111 and 112, respectively, in the manner shown inFIG. 1. The outputs of balanced detectors 111 and 112 are amplified by arespective one of amplifiers 121 and 122, and they may then benormalized by one of optional automatic-gain controllers (AGCs) 131 and132.

Balanced intensity detectors 111 and 112 are conventional. Typically,each of balanced intensity detectors 111 and 112 is made up of a pair ofwell-matched photodiodes. Balanced intensity detectors 111 and 112convert the output of each of the arms of ODIs 105 and 106 to anelectrical representation. Thus, balanced intensity detectors 111 and112 obtain an electrical version of the real and imaginary parts of thecomplex waveform that contains the information about the phasedifferences between two time locations separated by ΔT in thepolarization component of the received optical signal supplied from PBS101 to 1×3 optical splitter 102.

Photodiode 115 performs conventional direct intensity detection, andthus obtains the intensity profile of E_(x′) in electronic form.

Amplifiers 121, 122, and 125 amplify the signals supplied as outputs bybalanced intensity detector 111, balanced intensity detector 112, andphotodiode 115, respectively. Typically, amplifiers 121, 122, and 125convert the current which is output by the various photodiodes ofbalanced intensity detector 111, balanced intensity detector 112, andphotodiode 115 to respective corresponding voltages. To this end,amplifiers 121, 122, and 125 may be trans-impedance amplifiers.Furthermore, amplifiers 121 and 122 may be differential amplifiers.After amplification, each of the outputs is typically single ended.Optional automatic-gain controllers (AGCs) 131, 132, and 135 may beemployed to normalize the electronic waveforms prior to digitization.

Analog-to-digital converters (ADCs) 141, 142, and 143 perform “digitalsampling” of the amplified signals to develop a digital representationof the amplified signals. ADCs 141, 142, and 145 typically have the sameresolution, e.g., 8 bits.

1×3 optical splitter 103, similar to 1×3 optical splitter 102,replicates the received optical signal so as to produce three copies.One of the three beams produced by 1×3 optical splitter 103 is suppliedto optical delay interferometer (ODI) 107, another of the three beamsproduced by 1×3 optical splitter 103 is supplied to ODI 108, and thelast beam is supplied to photodiode 116.

Together, ODIs 107 and 108 make up an I/Q ODI pair. The four outputs ofI/Q ODI pair made up of ODIs 107 and 108 are then detected by twobalanced detectors 113 and 114, respectively, in the manner shown inFIG. 1. The outputs of balanced detectors 113 and 114 are amplified by arespective one of amplifiers 123 and 124, and they may then benormalized by one of optional automatic-gain controllers (AGCs) 133 and134.

Balanced intensity detectors 113 and 114 are conventional. Typically,each of balanced intensity detectors 113 and 114 is made up of a pair ofwell-matched photodiodes. Balanced intensity detectors 113 and 114convert the output of each of the arms of ODIs 107 and 108 to anelectrical representation. Thus, balanced intensity detectors 113 and114 obtain an electrical version of the real and imaginary parts of thecomplex waveform that contains the information about the phasedifferences between two time locations separated by ΔT in thepolarization component of the received optical signal supplied from PBS101 to 1×3 optical splitters 103.

Photodiode 116 performs conventional direct intensity detection, andthus obtains the intensity profile of E_(y′) in electronic form.

Amplifiers 123, 124, and 126 amplify the signals supplied as outputs bybalanced intensity detector 113, balanced intensity detector 114, andphotodiode 116, respectively. Typically, amplifiers 123, 124, and 126convert the current which is output by the various photodiodes ofbalanced intensity detector 113, balanced intensity detector 114, andphotodiode 116 to respective corresponding voltages. To this end,amplifiers 123, 124, and 126 may be trans-impedance amplifiers.Furthermore, amplifiers 123 and 124 may be differential amplifiers.After amplification, each of the outputs is typically single ended.Optional automatic-gain controllers (AGCs) 133, 134, and 136 may beemployed to normalize the electronic waveforms prior to digitization.

Analog-to-digital converters (ADCs) 143, 144, and 146 perform “digitalsampling” of the amplified signals to develop a digital representationof the amplified signals. ADCs 143, 144, and 146 typically have the sameresolution, e.g., 8 bits.

Digital signal processing unit 150 receives the digital representationof all of the digitized signals supplied from ADCs 141-146 and developsat least one so-called “generic” polarization component of the receivedoptical. Note that by a generic polarization component it is generallyintended the original signal that corresponds to the received signal atthe point at which the modulation of that polarization component fortransmission is completed.

In accordance with an aspect of the invention, reconstruction unit 151-1receives the digitized signals supplied from ADCs 141, 142, and 145 anddevelops a digital representation of the amplitude and phase profiles ofone of the polarizations of the received optical signal, e.g., x′.Similarly, in accordance with an aspect of the invention, reconstructionunit 151-2 receives the digitized signals supplied from ADCs 143, 144,and 146 and develops a digital representation of the received opticalsignal field, i.e., the amplitude and phase profiles, of one of theother polarization of the received optical signal, e.g., y′. To thisend, reconstruction unit 151-1 treats its inputs as if they were theentirety of the optical signal and processes those inputs according toLiu-Wei, e.g., using m=1, prior to any compensation for distortions,e.g., according to the processing described in Liu-Wei in connectionwith reconstruction unit 151 thereof. The resulting output for thisreconstruction, referred to in Liu-Wei as E_(R)(t_(s)), is referred toherein as E_(x′)(t). Similarly, reconstruction unit 151-2 treats itsinputs as if they were the entirety of the optical signal and processesthose inputs according to according to Liu-Wei, e.g., using m=1, priorto any compensation for distortions, e.g., according to the processingdescribed in Liu-Wei in connection with reconstruction unit 151 thereof,to develop received optical signal field, i.e., the amplitude and phaseprofiles. The resulting output for this reconstruction, referred to inLiu-Wei as E_(R)(t_(s)), is referred to herein as E_(y′)(t).

Due to fiber birefringence or PMD, the two orthogonal polarizationcomponents of the optical signal as received at the receiver after fibertransmission are generally not the generic polarization components ofthe signal. Therefore, in accordance with an aspect of the invention,the reconstructed digital versions of the complex field of each of thetwo orthogonal polarization components of the optical signal as receivedat the receiver E_(x′)(t) and E_(y′)(t) need to be further processedjointly to develop at least one “generic” polarization component of thereceived optical, as to be described below.

FIG. 4 shows an exemplary polarization “evolution” as an optical signalpasses over a typical fiber transmission link 402 that causes PMD. Thetwo polarization components of the signal after fiber transmission alongthe two PSP axes of the fiber, defined hereafter as E_(∥) ^(out) andE_(⊥) ^(out)—treating the fiber as a single DGD element that introducesa certain DGD between the two axes—can be linked to the two orthogonalcomponents of the received signal field E_(x′) and E_(y′) as follows,

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{E_{}^{out}(t)} \\{E_{\bot}^{out}(t)}\end{bmatrix} = {\begin{bmatrix}{\cos\left( \theta_{2} \right)} & {\sin\left( \theta_{2} \right)} \\{- {\sin\left( \theta_{2} \right)}} & {\cos\left( \theta_{2} \right)}\end{bmatrix} \cdot \begin{bmatrix}{E_{x^{\prime}}(t)} \\{{E_{y^{\prime}}(t)} \cdot {\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}\end{bmatrix}}} \\{{= \begin{bmatrix}{{{\cos\left( \theta_{2} \right)}{E_{x^{\prime}}(t)}} + {{\sin\left( \theta_{2} \right)}{{E_{y^{\prime}}(t)} \cdot {\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}}} \\{{{- {\sin\left( \theta_{2} \right)}}{E_{x^{\prime}}(t)}} + {{\cos\left( \theta_{2} \right)}{{E_{y^{\prime}}(t)} \cdot {\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}}}\end{bmatrix}},}\end{matrix} & (2)\end{matrix}$where θ₂ is the angle between the two characteristic orientations of PBS101 and the two PSP axes of fiber 402, and δφ₂ is the additional phasedifference between the two reconstructed signal fields E_(x′) and E_(y′)as compared to the phase difference of the two received polarizationcomponents right after PBS 403. The additional phase difference includesan initially unknown relative phase difference between the two referencepoints used in the two reconstructed optical fields. In accordance withan aspect of the invention, during the joint processing the phasedifference δφ₂ is determined by employing a searching technique, such asis described hereinbelow. E_(x′) and E_(y′) are the reconstructedoptical fields of the two orthogonal polarization components of thereceived optical signal as separated by polarization beam splitter 403.

The two polarization components of the signal along the two PSP axes offiber 402 at the input of fiber 402, defined hereafter as E_(∥) ^(in)and E_(⊥) ^(in), can be related to E_(∥) ^(out) and E_(⊥) ^(out) asE _(∥) ^(in)(t)=E _(∥) ^(out)(t−τ _(DGD))·e ^(j·δφ),E _(⊥) ^(in)(t)=E _(⊥) ^(out)(t),  (3)where τ_(DGD) is the PMD-induced DGD, and δφ is the PMD-induced orbirefringence-induced phase difference between the two PSPs, which maybe time varying, e.g., due to environmental, e.g., mechanical ortemperature changes. Conventionally, the ∥ and ⊥ axes are called thefast PMD axis and the slow PMD axis, respectively. In the case that PMDis sufficiently small, τ_(DGD) can be approximated as 0 in Eq. (3), butthe PMD-induced or birefringence-induced phase difference δφ cannot beneglected.

When the original signal emitted from transmitter 401 is polarizationmultiplexed to carry two generic polarization components, E_(x) andE_(y), the two generic components can be linked to E_(∥) ^(in) and E_(⊥)^(in) as

$\begin{matrix}{{\begin{bmatrix}{E_{x}(t)} \\{E_{y}(t)}\end{bmatrix} = {\begin{bmatrix}{\cos\left( \theta_{1} \right)} & {- {\sin\left( \theta_{1} \right)}} \\{\sin\left( \theta_{1} \right)} & {\cos\left( \theta_{1} \right)}\end{bmatrix} \cdot \begin{bmatrix}{E_{}^{i\; n}(t)} \\{E_{\bot}^{i\; n}(t)}\end{bmatrix}}},} & (4)\end{matrix}$where θ₁ is the angle between the two orthogonal polarization componentsof the original signal from the transmitter and the two PSP axes of thefiber at its input.

Combing equations (2), (3), and (4), two generic polarizationcomponents, E_(x) and E_(y), can then be expressed in terms of thereceived polarization components as

$\quad\begin{matrix}\begin{matrix}{\begin{bmatrix}{E_{x}(t)} \\{E_{y}(t)}\end{bmatrix} = {\begin{bmatrix}{\cos\left( \theta_{1} \right)} & {- {\sin\left( \theta_{1} \right)}} \\{\sin\left( \theta_{1} \right)} & {\cos\left( \theta_{1} \right)}\end{bmatrix} \cdot \begin{bmatrix}{E_{}^{i\; n}(t)} \\{E_{}^{i\; n}(t)}\end{bmatrix}}} \\{= {\begin{bmatrix}{\cos\left( \theta_{1} \right)} & {- {\sin\left( \theta_{1} \right)}} \\{\sin\left( \theta_{1} \right)} & {\cos\left( \theta_{1} \right)}\end{bmatrix} \cdot \begin{bmatrix}{{E_{}^{out}\left( {t - \tau_{DGD}} \right)} \cdot {\mathbb{e}}^{j \cdot {\delta\phi}}} \\{E_{\bot}^{out}(t)}\end{bmatrix}}} \\{= \begin{bmatrix}{{{\cos\left( \theta_{1} \right)}{{E_{}^{out}\left( {t - \tau_{DGD}} \right)} \cdot {\mathbb{e}}^{j \cdot {\delta\phi}}}} - {{\sin\left( \theta_{1} \right)}{E_{\bot}^{out}(t)}}} \\{{{\sin\left( \theta_{1} \right)}{{E_{}^{out}\left( {t - \tau_{DGD}} \right)} \cdot {\mathbb{e}}^{j \cdot {\delta\phi}}}} + {{\cos\left( \theta_{1} \right)}{E_{\bot}^{out}(t)}}}\end{bmatrix}} \\{= {\begin{bmatrix}{{{{\cos\left( \theta_{1} \right)}\left\lbrack {{{\cos\left( \theta_{2} \right)}{E_{x^{\prime}}\left( {t - \tau_{DGD}} \right)}} + {{\sin\left( \theta_{2} \right)}{{E_{y^{\prime}}\left( {t - \tau_{DGD}} \right)} \cdot {\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}}} \right\rbrack}{\mathbb{e}}^{j \cdot {\delta\phi}}} - {{\sin\left( \theta_{1} \right)}\left\lbrack {{{- {\sin\left( \theta_{2} \right)}}{E_{x^{\prime}}(t)}} + {{\cos\left( \theta_{2} \right)}{E_{y^{\prime}}(t)}{\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}} \right\rbrack}} \\{{{{\sin\left( \theta_{1} \right)}\left\lbrack {{{\cos\left( \theta_{2} \right)}{E_{x^{\prime}}\left( {t - \tau_{DGD}} \right)}} + {{\sin\left( \theta_{2} \right)}{{E_{y^{\prime}}\left( {t - \tau_{DGD}} \right)} \cdot {\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}}} \right\rbrack}{\mathbb{e}}^{j \cdot {\delta\phi}}} + {\cos{\left( \theta_{1} \right)\left\lbrack {{{- {\sin\left( \theta_{2} \right)}}{E_{x^{\prime}}(t)}} + {{\cos\left( \theta_{2} \right)}{E_{y^{\prime}}(t)}{\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}} \right\rbrack}}}\end{bmatrix}.}}\end{matrix} & (5)\end{matrix}$In the case that the original signal is singly polarized, i.e., it hasonly one generic polarization component at the transmitter, e.g., E_(x),only half of the computation in Eq. (5) is needed.

As shown in Eq. (5), five parameters, θ₁, θ₂, δφ, δφ₂, and τ_(DGD), aregenerally needed to recover the original optical signal field, which canbe either single polarized or polarization multiplexed. When PMD issufficiently small, e.g., the PMD induced DGD is much smaller than thesignal symbol period, τ_(DGD) may be safely set to zero in deriving theoriginal signal field, leaving four parameters, θ₁, θ₂, δφ, and δφ₂, tobe determined. Since these parameters are generally time varying, it isneeded to find the values of these parameters dynamically.

The digital signal processing needed to recover the generic polarizationcomponents from the reconstructed optical fields of the two orthogonalpolarization components of the received optical signal can be performedon a block by block basis, with each block having multiple samples. FIG.5 shows an exemplary arrangement to perform the digital signalprocessing needed to recover the generic polarization components fromthe reconstructed optical fields of the two orthogonal polarizationcomponents of the received optical signal, in accordance with an aspectof the invention. This circuit consists of demultiplexers 501 and 502, Mprocessing units (PUs) 505, and multiplexers 503 and 504.

The inputs to the arrangement of FIG. 5 are E_(x′)(t) and E_(y′)(t) andthe outputs therefrom are E_(x)(t) and E_(y)(t). Each of demultiplexers501 and 502 divides the samples it receives over M parallel paths,thereby reducing the processing speed requirement of Pus 505. Eventuallymultiplexers 503 and 504 multiplex the processed samples to constructE_(x)(t) and E_(y)(t). Note that at any given time, the blocks ofsamples supplied to one of PUs 505 may have samples overlapping withthose of its adjacent PUs. Note also that the multiplexers anddemultiplexers can be shared with the field reconstruction process,e.g., as described in Liu-Wei.

FIG. 6 shows an exemplary high level block diagram of arrangement 600which is suitable to be used to make up each of PUs 505. Arrangement600, when employed as a PU 505, receives at one time, for each timeperiod, two corresponding blocks of samples, each block being of lengthN. N is typically greater than 4 and less than 40, with a suitable valuebeing about 10. The value selected for N represents a tradeoff betweenaccuracy achievable and the speed of computation needed to process thesamples. The received samples are supplied to feed-forward subprocessor601 and real-time subprocessor 602. Feed-forward subprocessor 601 findsthe best guesses of the parameters needed to recover E_(x)(t) andE_(y)(t), and feeds these parameters, except for δφ₂, to real-timesubprocessor 602. Real-time subprocessor 602 receives N pairs ofE_(x′)(t) and E_(y′)(t) samples, as well as the best guesses ofparameters θ₁, θ₂, δφ, and τ_(DGD), which were determined byfeed-forward path 601, and supplies as an output the N pairs of E_(x)(t)and E_(y)(t) samples after processing the received inputs as describedhereinbelow.

FIG. 7 shows an exemplary process expressed in flow-chart form forfinding the best guesses of the parameters needed to recover E_(x)(t)and E_(y)(t), in accordance with an aspect of the invention. Thisprocess may be performed in feed-forward subprocessor 601. The processbegins in step 702, when N pairs of E_(x′)(t) and E_(y′)(t) samples arereceived. Next, in step 703, using Eq. (5), candidate values of E_(x)(t)and E_(y)(t) are calculated for each of the received N pairs ofE_(x′)(t) and E_(y′)(t) samples. To do so, for each E_(x′)(t) andE_(y′)(t) pair, a candidate value is calculated for each possiblecombination of values for each of the five parameters over theirrespective physically allowable ranges. For example, the physicallyallowable ranges may be θ₁ ε [0,π), θ₂ε [0,π), δφε [0,2π), and δφ₂ ε[0,2π). For τ_(DGD) the range employed may be from 0 to the symbolperiod of the signal, although it is recognized that τ_(DGD) mayactually be larger.

Preferably, this is performed by selecting a combination of values foreach of the five parameters and using them to compute N candidate valuesof E_(x)(t) and E_(y)(t). In one embodiment of the invention, the guessvalues for each of the parameters are uniformly distributed over withinits allowed range. Typically, 10 to 20 guess values for each parametershould be sufficient.

One way to perform the calculation is to implement double loop, wherethe outer loop is the parameter values and the inner loop is the Nsample pairs. A loop so arranged facilitates the computation of step704, in which the particular values of the five parameters thatminimizes a variance-type quantity of the N candidate E_(x)(t) andE_(y)(t) is selected. For example, the values of the five parametersthat minimizes the variance of a candidate set of

${E_{x}(t)},{i.e.},{\sum\limits_{t = 1}^{N}\left\lbrack {{{E_{x}(t)}}^{2} - \overset{\_}{{{E_{x}(t)}}^{2}}} \right\rbrack^{2}}$is selected as the best guess. Alternatively, the values of the fiveparameters that minimizes the variance of a candidate set of

${E_{y}(t)},{i.e.},{\sum\limits_{t = 1}^{N}\left\lbrack {{{E_{y}(t)}}^{2} - \overset{\_}{{{E_{y}(t)}}^{2}}} \right\rbrack^{2}}$is selected as the best guess. Alternatively, some combination of thetwo variances may be specified as variance-type quantity to beminimized.

The forgoing selection of the generic polarization components of thesignal, i.e., E_(x)(t) and E_(y)(t,) assumes that as originallytransmitted the generic polarization components intrinsically had aconstant intensity, i.e., amplitude, which is generally the case forDPSK-type formats, which include at least DBPSK and DQPSK.Alternatively, the best guesses of these parameters may be found usingapproaches similar to or based on the constant modulus algorithm (CMA).

In step 705, the best guesses for the four parameters θ₁, θ₂, δφ, andτ_(DGD) are supplied as an output, and control passes back to step 702to process the next N pairs of E_(x′)(t) and E_(y′)(t) samples. Notethat the values of the four parameters θ₁, θ₂, δφ, and τ_(DGD) typicallytend to change at a rate that is much slower than the signal symbolrate. Thus, feed-forward subprocessor 601 need not process all of theblocks of N pairs of E_(x′)(t) and E_(y′)(t) samples that it receives,since doing so will yield essentially the same values for those periodsof time over which the parameters remain substantially unchanged. Forexample, the rate of fiber PMD change is usually slower than 10 KHz,which is 10⁶ times slower than the symbol rate of a 10-Gbaud signal.Advantageously, this significantly relaxes the computation speedrequired feed-forward subprocessor 601. Of course, should there be asituation in which the rate of change of the values of four parametersθ₁, θ₂, δφ, and τ_(DGD) is more rapid, they may be computed more often,or even for every block.

In another embodiment of the invention, rather than use 10 to 20 guessesfor each of the slow varying parameters, θ₁, θ₂, δφ, and τ_(DGD) onlythree guess values are employed for each parameter, one being theprevious best guess value and the other two being its nearestneighboring guess values. For the angular parameters, the nearestneighbor guess values should be the cyclic neighbors, by which it isgenerally meant taking modulus with respect to the appropriate value,e.g., 2π for δφ and π for θ₁ and θ₂. The cyclic spacing between the twonearest neighboring guess values should be much smaller than theallowable range of the parameter. Preferably, the spacing is at least 10times smaller than the allowable range of the parameter. For τ_(DGD) thenearest neighbors are those values that are one minimum step up and oneminimum step down, each step being substantially smaller than the symbolperiod. Preferably, the spacing is at least 5 times smaller than theallowable range of the parameter. Doing so advantageously reduces theamount of computation that is required.

In yet another embodiment of the invention, the guess value for τ_(DGD)does not need to be searched. Rather, the guess value for τ_(DGD) can befixed to a fraction of the symbol period, e.g., 0.4 T_(S), and usefulPMD compensation still results.

FIG. 8 shows an exemplary process, expressed in flow-chart form, whichis performed by real-time subprocessor 602 in one embodiment of theinvention. In step 802, N pairs of E_(x′)(t) and E_(y′)(t) samples, aswell as the best guesses of parameters θ₁, θ₂, δφ, and τ_(DGD) obtainedby feed-forward subprocessor 601, are received. Next, step 803 computesE_(x)(t) and E_(y)(t) for a set of guess values of δφ₂ ε [0, 2π) usingEq. (5).

Thereafter, in step 804, the best guess of δφ₂ is found. In oneembodiment of the invention, the best guess is the guess by which atleast one of the variance of the N quantities that represents

${E_{x}(t)},{i.e.},{\sum\limits_{t = 1}^{N}\left\lbrack {{{E_{x}(t)}}^{2} - \overset{\_}{{{E_{x}(t)}}^{2}}} \right\rbrack^{2}},$and that represents E_(y)(t), i.e.,

${E_{y}(t)},{i.e.},{\sum\limits_{t = 1}^{N}\left\lbrack {{{E_{y}(t)}}^{2} - \overset{\_}{{{E_{y}(t)}}^{2}}} \right\rbrack^{2}},$is minimized. Note that typically minimizing one of variance of the Nquantities that represents E_(x)(t) and variance of the N quantitiesthat represents E_(y)(t) results in the other also being minimized.However, this is not always so, e.g., in the presence of noise, and theimplementer may instead choose to minimize the difference between thevariance of the N quantities that represents E_(x)(t) and the varianceof the N quantities that represents E_(y)(t).

In step 805 the N pairs of E_(x)(t) and E_(y)(t) samples that correspondto the best guess of δφ₂ are supplied as outputs and control passes backto step 802 to process the next N pairs of E_(x′)(t) and E_(y′)(t)samples.

FIG. 9 shows an exemplary high level block diagram arrangement 900 thatis suitable to be used to make up each of PUs 505 but which is arrangedto speed up the processing as compared to the arrangement shown in FIG.6. The arrangement of FIG. 9 takes into consideration the fact thatparameters θ₁, θ₂, and τ_(DGD) typically change much more slowly than δφchanges, and therefore they may to be computed at a slower rate. To thisend feed-forward subprocessor 601 of FIG. 6 is further split into firstfeed-forward subprocessor 901, which computes at a slower rate ascompared to feed-forward subprocessor 601 of FIG. 6, and secondfeed-forward subprocessor 903, which computes at the same rate as didfeed-forward subprocessor 601 of FIG. 6.

First feed-forward subprocessor 901 receives as input N pairs ofE_(x′)(t) and E_(y′)(t) samples and supplies as outputs the best guessesof parameters θ₁, θ₂, and τ_(DGD). Second feed-forward subprocessor 903likewise receives as input N pairs of E_(x′)(t) and E_(y′)(t) samplesand it also receives as input the best guesses of θ₁, θ₂, and τ_(DGD)which are supplied as outputs by first feed-forward subprocessor 901.Second feed-forward subprocessor 903 supplies the best guess value of δφas an output to real-time subprocessor 602 and it also passes on thebest guesses of θ₁, θ₂, and τ_(DGD). Note that, alternatively, the bestguesses of θ₁, θ₂, and τ_(DGD) could be supplied directly from firstfeed-forward subprocessor 901 to real-time subprocessor 602.Advantageously, since the update rate of first feed-forward subprocessor901 can be much slower than that of second feed-forward subprocessor903, the computational speed requirement of the feed-forward path isreduced overall.

Real-time subprocessor 602 receives the same N pairs of E_(x′)(t) andE_(y′)(t) samples and the best guesses of parameters θ₁, θ₂, δφ, andτ_(DGD) as it did in FIG. 6, albeit from second feed-forwardsubprocessor 903 rather than feed-forward subprocessor 601, and outputsthe N pairs of E_(x)(t) and E_(y)(t) samples based on the signalprocessing as described hereinabove.

The effectiveness of the electronic PMD compensation (PMDC) describedhereinabove can be further improved by treating the fiber as if it wasmade up of multiple segments, each of which has its own “virtual” DGDparameters. More specifically, instead of the three parameters θ₁, δφ,and τ_(DGD) previously used to describe the fiber-induced PMD, one cantreat the fiber link as a concatenation of M PMD segments, i.e., minifibers, each described by three parameters, θ₁ ^(i), δφ^(i), and τ_(DGD)^(i) where i=1, 2, . . . M is the index of the virtual PMD segment. Thetwo received polarization components can be generally linked to thegeneric polarization components, E_(x) and E_(y), as

$\begin{matrix}{{\begin{bmatrix}E_{x^{\prime}} \\E_{y^{\prime}}\end{bmatrix} = {{T \cdot \begin{bmatrix}E_{x} \\E_{y}\end{bmatrix}} = {P \cdot R_{2} \cdot {\prod\limits_{i = 1}^{M}{{PMD}^{M - i + 1} \cdot \begin{bmatrix}E_{x} \\E_{y}\end{bmatrix}}}}}},} & (6)\end{matrix}$where matrix T represents the polarization transformation of the fiberlink, R₂ is the rotation matrix associated with the projection of thesignal components along the fiber PMD PSP axes at the fiber output onthe polarization axes of the PBS used in the receiver, PMD^(i) is thematrix describing the PMD effect of the i-th segment, and P is aphase-delay matrix representing the additional phase delay between thetwo reconstructed fields after the polarization beam splitting at thereceiver.

Using the notations shown in FIG. 4, the rotation matrix R₂ can bewritten as

$\begin{matrix}{R_{2} = {\begin{bmatrix}{\cos\left( \theta_{2} \right)} & {- {\sin\left( \theta_{2} \right)}} \\{\sin\left( \theta_{2} \right)} & {\cos\left( \theta_{2} \right)}\end{bmatrix}.}} & (7)\end{matrix}$The phase-delay matrix P can be written as

$\begin{matrix}{P = {\begin{bmatrix}1 & 0 \\0 & {\mathbb{e}}^{j \cdot {\delta\phi}_{2}}\end{bmatrix}.}} & (8)\end{matrix}$The PMD matrix of the i-th segment, PMD^(i), can be written in thefrequency domain, e.g., after a Fourier transform from the time domain,as

$\begin{matrix}{{{{PMD}^{i}\left( {\Delta\; f} \right)} = {\begin{bmatrix}1 & 0 \\0 & {\mathbb{e}}^{j \cdot {({{2{\pi \cdot \Delta}\;{f \cdot \tau_{DGD}^{i}}} + {\delta\phi}^{i}})}}\end{bmatrix} \cdot \begin{bmatrix}{\cos\left( \theta_{1}^{i} \right)} & {\sin\left( \theta_{1}^{i} \right)} \\{- {\sin\left( \theta_{1}^{i} \right)}} & {\cos\left( \theta_{1}^{i} \right)}\end{bmatrix}}},} & (9)\end{matrix}$where τ_(DGD) ^(i) and δφ^(i) are, respectively, the differentialgroup-delay (DGD) and the phase delay between the two PSP axes of thei-th PMD segment, θ₁ ^(i) is the angle between the orientation of thesignal polarization at the input of the i-th PMD segment and one of itsPSP axes, and Δf is the frequency offset from the center frequency ofthe signal. In the time domain, the PMD matrix acts on an input signalas follows,

$\begin{matrix}{{PMD}^{i} \cdot {\quad{\begin{bmatrix}{E_{x}^{i - 1}(t)} \\{E_{y}^{i - 1}(t)}\end{bmatrix} = {\quad{\left\lbrack \begin{matrix}{{{\cos\left( \theta_{1}^{i} \right)}{E_{x}^{i - 1}(t)}} + {{\sin\left( \theta_{1}^{i} \right)}{E_{y}^{i - 1}(t)}}} \\{\left\lbrack {{{- {\sin\left( \theta_{1}^{i} \right)}}{E_{x}^{i - 1}\left( {t - \tau_{DGD}^{i}} \right)}} + {{\cos\left( \theta_{1}^{i} \right)}{E_{y}^{i - 1}\left( {t - \tau_{DGD}^{i}} \right)}}} \right\rbrack{\mathbb{e}}^{j \cdot {\delta\phi}^{i}}}\end{matrix} \right\rbrack,}}}}} & (10)\end{matrix}$where E_(x) ^(i−1) and E_(y) ^(i−1) are the two orthogonal signalpolarization components along the two PSP axes of PMD segment i−1 itsoutput when i≧2, or the generic signal polarization components, E_(x)and E_(y), when i=1. In principle, when the polarization transformationmatrix T is known, the generic signal polarization components can thenbe derived from the reconstructed polarization components using

$\begin{matrix}{{\begin{bmatrix}E_{x} \\E_{y}\end{bmatrix} = {{T^{- 1} \cdot \begin{bmatrix}{E_{x^{\prime}}(t)} \\{E_{y^{\;\prime}}(t)}\end{bmatrix}} = {\prod\limits_{i = 1}^{M}{\left( {PMD}^{i} \right)^{- 1} \cdot R_{2}^{- 1} \cdot {P^{- 1}\begin{bmatrix}E_{x^{\prime}} \\E_{y^{\prime}}\end{bmatrix}}}}}},} & (11)\end{matrix}$where −1 indicates the standard matrix inverse operation, i.e., theproduct of a matrix and its inverse is the identity matrix I.

FIG. 10 shows exemplary high level block diagram of arrangement 1000suitable to be used to make up each of PUs 505 but which is arranged totreat the fiber as if it was made up of multiple segments, so as toachieve better compensation for PMD, including higher order PMD, thancan be achieved than using the arrangements of FIG. 6 or 9. The processfor performing such electronic PMDC assumes that the fiber was made upof M “virtual” PMD elements. Feed-forward subprocessor 1001 receives asinputs N pairs of E_(x′)(t) and E_(y′)(t) samples and supplies as itsoutput the best guesses of parameters θ₁ ¹, δφ¹, and τ_(DGD) ¹ . . . θ₁^(M), δφ^(M), and τ_(DGD) ^(M). Real-time subprocessor 1002 receives asinputs the N pairs of E_(x′)(t) and E_(y′)(t) samples as well as thebest guesses of the parameters supplied by feed-forward subprocessor1001, and supplies as outputs the N pairs of E_(x)(t) and E_(y)(t)samples using the methods described hereinabove.

As M increases, the PMDC capability also increases. However, the neededcomputation power to perform the PMDC calculations increases as well.Thus, there is a tradeoff between required computation power and thePMDC that is performed. Note that oftentimes setting M=2 is sufficientto provide better than first order PMD compensation without requiring asevere increase in processing power. For further simplification, theguess values for τ_(DGD) ¹ . . . τ_(DGD) ^(M) can be fixed to a fractionof the symbol period, e.g., 0.4 T_(S), as noted hereinabove.

FIG. 11 shows high level block diagram of arrangement 1100 suitable tobe used to make up each of PUs 505 but which is arranged to treat thefiber as if it was made up of 2 segments each having DGD values eachfixed to 0.4 T_(S).

Note that, in accordance with an aspect of the invention, the digitalPMD compensation schemes described above may also be employed withso-called “dual-polarization coherent-detection” receivers, wheredigital representations of two orthogonal polarization components of thereceived optical signal are obtained. A typical dual-polarizationcoherent-detection receiver with DSP is shown in “UncompensatedTransmission of 86 Gbit/s Polarization Multiplexed RZ-QPSK over 100 kmof NDSF Employing Coherent Equalization” by Fludger et al., which waspublished as ECOC'06 post-deadline paper Th4.3.3, which is incorporatedby reference as if fully set forth herein. FIG. 12 shows an exemplaryhigh level block diagram of arrangement 1200 which is suitable to beused to make up each of PUs 505 but which is arranged for use with acoherent-detection receiver, in accordance with an aspect of theinvention.

As is well known, such coherent detection receivers employ, an opticallocal oscillator (OLO) that provides an absolute phase reference forboth received polarization components. As a result, there is nouncertainty in the additional phase difference δφ₂ due to the fieldreconstruction process. Consequently, δφ₂ does not need to be estimatedin real-time subprocessor 1202, and instead can be estimated infeed-forward subprocessor 1201 so that the computational effort in thereal-time subprocessor is much reduced. Typically, δφ₂ changes at a verylow speed, e.g., <1 KHz, so feed-forward subprocessor 1201 only needs toupdate δφ₂ at a much lower speed than the signal date rate.

FIG. 13, similar to FIG. 8, shows an exemplary process, expressed inflow-chart form, that is performed in real-time subprocessor 1202, inone embodiment of the invention. In step 1302 N pairs of E_(x′)(t) andE_(y′)(t) samples, as well as the best guesses of parameters θ₁, θ₂, δφ,δφ₂, and τ_(DGD) for each of M virtual segments obtained by feed-forwardsubprocessor 1201, are received. Next, step 1303 computes E_(x)(t) andE_(y)(t) using Eq. (11). In step 1305 the N pairs of E_(x)(t) andE_(y)(t) samples are supplied as outputs and control passes back to step1302 to process the next N pairs of E_(x′)(t) and E_(y′)(t) samples.

As mentioned hereinabove, to simplify, the DGD values can be fixed,e.g., each equal to about 0.4 Ts. Also, M can be chosen to be 2.

Once the original signal field is obtained, further compensation forother impairments, e.g., chromatic dispersion and/or self-phasemodulation, and data recovery following suitable demodulation, can beperformed to extract the data content from at least on genericpolarization, using compensation for other impairments unit 152,demodulation unit 154, and data recovery unit 155.

A practical issue with the use of differential detection is that itemploys ODIs, which typically exhibit polarization-dependent phase shift(PDPS). In other words, generally, the phase offset between the two armsof an ODI, φ, is dependent on the polarization state of the opticalsignal. When the signal polarization is aligned with one of the twocharacteristic polarization orientations of the ODI, the phase offset φreaches its maximum or its minimum. The PDPS is the difference betweenthe maximum and the minimum phase offsets.

There are three common types of ODI: 1) fiber-based, 2) planar lightwavecircuit (PLC)-based, and 3) free-space optics-based. The PDPS of afiber-based ODI is typically due to the birefringence of the fiberresulting from mechanical stress. The PDPS of a PLC-based ODI istypically due to the birefringence of the waveguide structure of thePLC. The PDPS of a free-space optics based ODI is typically due to thepolarization-dependent phase delay of the beam splitter used in formingthe two optical interference paths. The PDPS can range from about 2degrees (0.035 rad.) to about 20 degrees (0.35 rad.), the particularvalue for any ODI depending on its design.

The field reconstruction process as described herein relies on the phasedifference estimation at multiple sampling locations. If the signalpolarization is not aligned with one of the two characteristicpolarization orientations of the ODI, the PDPS will accumulate as thenumber of sampling points increases and prevent accurate phaseestimation. Thus, it is preferred to align PBS 101 in such a way thatthe polarization of each of the two split signals, i.e., E_(x′) andE_(y′) is aligned with one of the two characteristic polarizationorientations of the ODIs. This can be achieved by using, e.g., 1)polarization-maintaining fibers with suitable orientations to connectthe two outputs of PBS 101 with the two inputs of ODI pairs 105-106 and107-108, or 2) polarization-maintaining free space optical connectionsbetween PBS 101 and the two inputs of ODI pairs 105-106 and 107-108 whenthe ODIs are free-space optics based.

FIG. 2 shows an embodiment of the invention similar to that shown inFIG. 1 but in which the intensity detection branches are omitted. Inaccordance with an aspect of the invention, the intensity profile foreach polarization component is approximated from the absolute value ofits respective one of the complex waveforms rather than directlyrecovered from the received optical signal.

FIG. 3 shows another embodiment of the invention similar to that shownin FIG. 1 but which employs only a single I/Q ODI pair. This is achievedby eliminating PBS 101 of FIG. 1 and employing in lieu thereof four PBSs301 at the four outputs of the first I/Q ODI. Furthermore, as in FIG. 2,the intensity detection branches are omitted and the intensity profilefor each polarization component is approximated rather than directlyrecovered from the received optical signal. Advantageously, the cost ofthe overall arrangement, as with respect to the arrangement of FIG. 1,is significantly reduced.

In the embodiment of FIG. 3 the received signal is supplied directlyinto a single polarization-independent I/Q ODI pair made up of ODIs 305and 306, whose four outputs are each connected to a respective one ofPBSs 301 with the same polarization orientation. The eight outputs fromPBSs 301, consisting of four x′-polarized outputs and four y′-polarizedoutputs, are then treated in the same manner as the outputs of the I/QODI pairs of FIG. 1, i.e., detected by balanced detectors whose outputsare sampled, after optional amplification and gain control, by arespective ADC. The sampled waveforms are then processed to obtain adigital representation of the signal optical field as describedhereinabove.

As will be readily understood by those of ordinary skill in the art, theinstant invention may be applied to optical differential phase-shiftkeying (DPSK) signals, such as differential binary phase-shift keying(DBPSK) and differential quadrature phase-shift keying (DQPSK) signals,since ODI(s) and balanced detection are commonly used for DPSKdetection. Furthermore, this invention may also be applied toamplitude-shift keying (ASK), combined DPSK/ASK, and differential QAM.

What is claimed is:
 1. An optical receiver, comprising: adual-polarization direct differential receiver portion that supplies asan output electronic analog representations of real and imaginary partsof two complex waveforms each of which contains information about phasedifferences between a plurality of time locations that are spaced by aprescribed amount for each respective one of two orthogonal polarizationcomponents of a received optical signal; and a signal processor, coupledto said dual-polarization direct differential detection receiverportion, for developing a digital representation of an intensity and aphase profile representing at least one generic polarization componentof said received optical signal.
 2. The invention as defined in claim 1wherein said signal processor develops said digital representation of anintensity and a phase profile representing at least one genericpolarization component of said received optical signal using informationfrom both of said electronic analog representations of said real andimaginary parts of said two complex waveforms.
 3. The invention asdefined in claim 1 wherein said signal processor further comprises:means for developing a digital representation of said optical field ofeach of said two orthogonal polarization components of said receivedoptical signal; and means for developing a digital representation of theoptical field of at least one generic polarization component of theoptical signal by jointly processing said digital representations ofsaid optical fields of said two orthogonal polarization components ofsaid received signal.
 4. The invention as defined in claim 1 whereinsaid two orthogonal polarization components of said received opticalsignal are defined by at least one polarization beam splitter.
 5. Theinvention as defined in claim 1 wherein said dual-polarization directdifferential detection receiver further comprises a direct intensitydetection unit to obtain an intensity profile of said received opticalsignal.
 6. The invention as defined in claim 5 wherein said directintensity detection unit is a photodiode.
 7. The invention as defined inclaim 1 further comprising an analog to digital converter unit, saidanalog to digital converter unit converting said real and imaginaryparts of said complex waveform to respective digital representationsthereof and supplying said digital representation of real and imaginaryparts of said complex waveform to said signal processor.
 8. Theinvention as defined in claim 7 further comprising an automatic gaincontrol unit interposed between said direct differential detectionreceiver and said analog to digital converter.
 9. The invention asdefined in claim 8 wherein said analog to digital converter unitincludes a plurality of analog to digital converters.
 10. The inventionas defined in claim 7 wherein said signal processor processes a group ofsamples of said digital representation of said real and imaginary partsof said complex waveform supplied by said analog to digital converterunit together.
 11. The invention as defined in claim 10 wherein the sizeof said group is proportional to the maximum number of interactingoptical symbols during optical transmission due to dispersive effects inan optical channel over which said received optical signal traveled. 12.The invention as defined in claim 1 wherein said signal processorfurther comprises means for compensating said digital representation ofan intensity and a phase profile representing at least one said genericpolarization component of said received optical signal for transmissionimpairment inflicted on said received optical signal by a channel overwhich said received optical field had traveled.
 13. The invention asdefined in claim 12 wherein said transmission impairment belongs to agroup consisting of: polarization-mode dispersion, chromatic dispersion,and fiber nonlinear effects.
 14. The invention as defined in claim 1wherein said signal processor further comprises means, responsive tosaid digital representation of an intensity and a phase profilerepresenting at least one said generic polarization component of saidreceived optical signal, for performing demodulation and data recovery.15. The invention as defined in claim 1 wherein said received opticalsignal was derived from two generic polarization components that wereorthogonal to each other in terms of polarization when transmittedtogether from a transmitter.
 16. The invention as defined in claim 1wherein said optical signal is a polarization-multiplexed signal thatcomprises two generic polarization components that are orthogonal toeach other.
 17. The invention as defined in claim 1 wherein said signalprocessor further comprises: a plurality of multiple parallel processingunits each of whose inputs are coupled to a data demultiplexer and whoseoutputs are coupled to a data multiplexer.
 18. The invention as definedin claim 17 wherein each of said processing units operates on ablock-by-block basis, wherein each block includes a plurality of samplesfrom each of said two orthogonal polarization components of saidreceived signal.
 19. The invention as defined in claim 17 wherein eachof said processing units operates in parallel, processing a block ofsamples that correspond to a time period, and wherein each block beingprocessed by a one of said processing units may contain samples thatare, were, or will also be processed by another one of said processingunits.
 20. The invention as defined in claim 1 wherein said signalprocessor further comprises: a processing unit operating on ablock-by-block basis, wherein each block includes a plurality of samplesfrom each of said two orthogonal polarization components of saidreceived signal, said processing unit further comprising at least onefeed-forward processor and at least one real time processor.
 21. Theinvention as defined in claim 20 wherein said feed-forward processorupdates outputs it supplies for use as inputs by said real-timeprocessor at a slower rate than a rate at which said real-time processorperforms calculations using said feed-forward processor outputs.
 22. Theinvention as defined in claim 20 wherein said feed-forward processordetermines values for θ₁, τ_(DGD), δφ, θ₂, δφ₂, where θ₁ is the anglebetween the two orthogonal polarization components of the originalsignal from the transmitter and the two PSP axes of the fiber at itsinput, τ_(DGD) is the PMD-induced DGD, δφ is the PMD-induced orbirefringence-induced phase difference between the two PSPs, θ₂ is theangle between the two characteristic orientations of a polarization beamsplitter used to separate orthogonal components of said received signaland the two principle state of polarization axes of a fiber from whichsaid received signal is received at said receiver, and δφ₂ is the phasedifference between the two reconstructed signal fields E_(x′) andE_(y′), but only supplies values for θ₁, τ_(DGD), δφ, θ₂ to saidreal-time processor.
 23. The invention as defined in claim 1 whereinsaid signal processor further comprises electronic polarizationdemultiplexing means for developing said at least one genericpolarization component of said received optical signal by jointlyprocessing said digital representations of said two orthogonalpolarization components of said received optical signal.
 24. Theinvention as defined in claim 23 wherein said electronic polarizationdemultiplexing means uses the following computation to obtain theoptical fields of the two generic polarization components E_(x)(t) andE_(y)(t) of said received optical signal ${\begin{bmatrix}{E_{x}(t)} \\{E_{y}(t)}\end{bmatrix} = \begin{bmatrix}{{{{\cos\left( \theta_{1} \right)}\left\lbrack {{{\cos\left( \theta_{2} \right)}{E_{x} \cdot \left( {t - \tau_{DGD}} \right)}} + {{\sin\left( \theta_{2} \right)}{E_{y} \cdot \left( {t - \tau_{DGD}} \right) \cdot {\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}}} \right\rbrack}{\mathbb{e}}^{j \cdot {\delta\phi}}} - {{\sin\left( \theta_{1} \right)}\left\lbrack {{{- {\sin\left( \theta_{2} \right)}}{E_{x^{\prime}}(t)}} + {{\cos\left( \theta_{2} \right)}{E_{y^{\prime}}(t)}{\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}} \right\rbrack}} \\{{{{\sin\left( \theta_{1} \right)}\left\lbrack {{{\cos\left( \theta_{2} \right)}{E_{x} \cdot \left( {t - \tau_{DGD}} \right)}} + {{\sin\left( \theta_{2} \right)}{E_{y} \cdot \left( {t - \tau_{DGD}} \right) \cdot {\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}}} \right\rbrack}{\mathbb{e}}^{j \cdot {\delta\phi}}} + {{\cos\left( \theta_{1} \right)}\left\lbrack {{{- {\sin\left( \theta_{2} \right)}}{E_{x^{\prime}}(t)}} + {{\cos\left( \theta_{2} \right)}{E_{y^{\prime}}(t)}{\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}} \right\rbrack}}\end{bmatrix}},$ where E_(x′) and E_(y′) are the reconstructed opticalfields of the into two orthogonal polarization components of saidreceived optical signal separated by a polarity beam splitter, θ₁ is theangle between the two orthogonal polarization components of the originalsignal from the transmitter and the two PSP axes of the fiber at itsinput, τ_(DGD) is the PMD-induced DGD, δφ is the PMD-induced orbirefringence-induced phase difference between the two PSPs, θ₂ is theangle between the two characteristic orientations of a polarization beamsplitter used to separate orthogonal components of said received signaland the two principle state of polarization axes of a fiber from whichsaid received signal is received at said receiver, and δφ₂ is the phasedifference between the two reconstructed signal fields E_(x′) andE_(y′), θ₁ is the angle between one of the two generic orthogonalpolarization components of the polarization-multiplexed signal at theinput of the PBS and the orientation of the PBS, and φ₁ is the opticalphase difference between the two generic polarization components at thePBS input.
 25. The invention as defined in claim 24 wherein saidelectronic polarization demultiplexing means adaptively optimizes valuesof parameters θ₁ and φ₁.
 26. The invention as defined in claim 24wherein said electronic polarization demultiplexing means adaptivelyoptimizes values of parameters θ₂, τ_(DGD), and φ₂.
 27. The invention asdefined in claim 1 wherein said dual-polarization direct differentialdetection receiver comprises at least one I/Q optical delayinterferometer pair.
 28. The invention as defined in claim 27 whereinsaid dual-polarization direct differential detection receiver furthercomprises at least one polarization beam splitter that supplies that isarranged to couple one of said two orthogonal polarization components ofsaid received optical signal to said at least one I/Q optical delayinterferometer pair.
 29. The invention as defined in claim 27 whereinsaid dual-polarization direct differential detection receiver furthercomprises at least one polarization beam splitter and wherein said atleast one I/Q optical delay interferometer pair is arranged to supply atleast one of its outputs to said at least one polarization beamsplitter.
 30. The invention as defined in claim 27 wherein said at leastone I/Q optical delay interferometer pair has a delay equal to aprescribed amount.
 31. The invention as defined in claim 27 wherein saiddelay of said I/Q ODI pair equals to the symbol period of one of saidgeneric polarization components of said received optical signal thatcarries a single data modulation.
 32. The invention as defined in claim27 wherein said delay of said I/Q ODI pair is a fraction of the symbolperiod of a one of said generic polarization component of said receivedoptical signal that carries a single data modulation.
 33. The inventionas defined in claim 27 wherein the in-phase (I) and quadrature (Q)branches of said I/Q ODI pair have a delay difference between them thatcorresponds to an optical phase difference of about π/2.
 34. Theinvention as defined in claim 27 wherein said dual-polarization directdifferential detection, receiver further comprises at least onepolarization beam splitter coupled to said I/Q ODI pair and the twocharacteristic polarization orientations of said I/Q ODI pair arealigned with the polarization orientations of the two outputs of saidoptical polarization beam splitter.
 35. The invention as defined inclaim 27 wherein said I/Q ODI pair has a polarization dependent phaseshift of less than about 3 degrees.
 36. The invention as defined inclaim 1 wherein said dual-polarization direct differential detectionreceiver further comprises four balanced intensity detectors, each ofsaid balanced intensity detectors being coupled to a respective one oftwo branches of said I/Q ODI pair for a respective one of twopolarization components separated by said polarization beam splitter.37. The invention as defined in claim 1 wherein said dual-polarizationdirect differential detection receiver portion comprises at least oneI/Q optical delay interferometer pair, at least one polarization beamsplitter, and, four balanced intensity detectors, each of said balancedintensity detectors being coupled to a respective output branch of saidat least one I/Q optical delay interferometer pair for a respective oneof two orthogonal polarization components of a received optical signalthat have been separated by said polarization beam splitter.
 38. Theinvention as defined in claim 37 wherein said dual-polarization directdifferential detection receiver portion further comprises four analog todigital converters that convert each output of said four balancedintensity detectors to a respective digital representation and whereinsaid signal processor is coupled to receive said digital representationsand to employ information from each of said digital representations todevelop said digital representation of an intensity and a phase profilerepresenting at least one generic polarization component of saidreceived optical signal.
 39. The invention as defined in claim 38wherein said at least one I/Q optical delay interferometer pair has adelay equal to about the inverse of the sampling rate of said fouranalog to digital converters.
 40. A method for use in an opticalreceiver, the method comprising the steps of: converting an opticalsignal that when received has two polarization components into a digitalrepresentation comprising an in phase and quadrature component for eachof said polarization components using a dual-polarization directdifferential receiver; and jointly processing said digitalrepresentation of said in phase and quadrature component for each ofsaid polarization components to develop therefrom a digitalrepresentation of an intensity and a phase profile representing at leastone generic polarization component of said received optical signal. 41.The invention as defined in claim 40 wherein said converting stepfurther comprises the steps of: separating said optical signal into atleast two polarization components; creating a copy of each of saidpolarization components of said received optical signal; delaying eachof said copies by a prescribed amount, and interfering each of saidcopies with its respective original so as to separate said in phase andquadrature component for each of said polarization components; anddigitizing in phase and quadrature component for each of saidpolarization components.
 42. The invention as defined in claim 40wherein said converting step further comprises the steps of: creating acopy of said received optical signal; delaying said copy by a prescribedamount, and interfering said copy with said received optical signal soas to separate said in phase and quadrature components for said receivedoptical signal; and separating each of said in phase and quadraturecomponents into at least two polarization components; and digitizing inphase and quadrature components for each of said polarizationcomponents.
 43. The invention as defined in claim 40 wherein said stepof jointly processing further comprises the step of grouping samples ofsaid digital representation of said in phase and quadrature componentfor each of said polarization components into blocks, wherein each blockincludes a plurality of samples from each of said polarizationcomponents of said received signal; and wherein, in said step of jointlyprocessing, said samples are processed on a block-by-block basis. 44.The invention as defined in claim 40 wherein said step of jointlyprocessing determines two generic polarization components E_(x)(t) andE_(y)(t) of said received optical signal ${\begin{bmatrix}{E_{x}(t)} \\{E_{y}(t)}\end{bmatrix} = \begin{bmatrix}{{{{\cos\left( \theta_{1} \right)}\left\lbrack {{{\cos\left( \theta_{2} \right)}{E_{x} \cdot \left( {t - \tau_{DGD}} \right)}} + {{\sin\left( \theta_{2} \right)}{E_{y} \cdot \left( {t - \tau_{DGD}} \right) \cdot {\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}}} \right\rbrack}{\mathbb{e}}^{j \cdot {\delta\phi}}} - {{\sin\left( \theta_{1} \right)}\left\lbrack {{{- {\sin\left( \theta_{2} \right)}}{E_{x^{\prime}}(t)}} + {{\cos\left( \theta_{2} \right)}{E_{y^{\prime}}(t)}{\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}} \right\rbrack}} \\{{{{\sin\left( \theta_{1} \right)}\left\lbrack {{{\cos\left( \theta_{2} \right)}{E_{x} \cdot \left( {t - \tau_{DGD}} \right)}} + {{\sin\left( \theta_{2} \right)}{E_{y} \cdot \left( {t - \tau_{DGD}} \right) \cdot {\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}}} \right\rbrack}{\mathbb{e}}^{j \cdot {\delta\phi}}} + {{\cos\left( \theta_{1} \right)}\left\lbrack {{{- {\sin\left( \theta_{2} \right)}}{E_{x^{\prime}}(t)}} + {{\cos\left( \theta_{2} \right)}{E_{y^{\prime}}(t)}{\mathbb{e}}^{j \cdot {\delta\phi}_{2}}}} \right\rbrack}}\end{bmatrix}},$ where E_(x′) and E_(y′) are reconstructed opticalfields of said orthogonal polarization components of said receivedoptical signal after separation by a polarization beam splitter, θ₁ isthe angle between the two orthogonal polarization components of anoriginal signal from a transmitter from which a signal that is receivedas said received signal is transmitted over a fiber having two principlestate of polarization axes at its input, τ_(DGD) is thepolarization-mode dispersion (PMD)-induced differential group delay(DGD), δφ is the PMD-induced or birefringence-induced phase differencebetween the two PSPs, θ₂ is the angle between the two characteristicorientations of said polarization beam splitter and the two principlestate of polarization axes of said fiber, and δφ₂ is the phasedifference between the two reconstructed signal fields E_(x′) andE_(y′), θ₁ is the angle between one of the two generic orthogonalpolarization components of the polarization-multiplexed signal at theinput of said polarization beam splitter and the orientation of the saidpolarization beam splitter, and φ₁ is the optical phase differencebetween the two generic polarization components at the said polarizationbeam splitter input.
 45. An optical receiver, comprising: adual-polarization direct differential receiver that comprises: at leastone I/Q optical delay interferometer pair having four output branches;at least one polarization beam splitter; four balanced intensitydetectors; and four analog to digital converters; said at least one I/Qoptical delay interferometer, said at least one polarization beamsplitter, said four balanced intensity detectors, and four analog todigital converters being arranged so as to produce an in phase andquadrature component for each of polarization component of a receivedoptical signal that when received has two polarization components asignal processor, coupled to said four analog to digital converters fordeveloping a digital representation of an intensity and a phase profilerepresenting at least one generic polarization component of saidreceived optical signal using information from both of said digitalrepresentations of said real and imaginary parts of said polarizationcomponents of said received optical signal supplied as output by saidanalog to digital converters.
 46. The invention as defined in claim 45wherein said signal processor further comprises: a plurality of multipleparallel processing units each of whose inputs are coupled to a datademultiplexer and whose outputs are coupled to a data multiplexer. 47.The invention as defined in claim 45 wherein said signal processorfurther comprises: a processing unit operating on a block-by-blockbasis, wherein each block includes a plurality of samples from each ofsaid two orthogonal polarization components of said received signal,said processing unit further comprising at least one feed-forwardprocessor and at least one real time processor.